Abstract
In this paper, we investigate an SIR epidemic model with varying population sizes and regime switching in a two patch setting. Sufficient conditions for extinction and persistence in the mean of the diseases are obtained. In addition, we establish sufficient conditions for the existence of positive recurrence of the solutions to the model in the case of persistence by constructing a suitable stochastic Lyapunov function with regime switching. Finally, numerical simulations are performed to test our theory conclusion.
•An SIR epidemic model with regime switching in a two patch setting is proposed.•The dynamic behaviors of the system are studied.•We establish sufficient conditions for extinction and persistence of the diseases.•The existence of positive recurrence of the solutions to the model is obtained.•Numerical simulations are performed to test our theory conclusion.